Error Estimates For A Linear Folding Model

TL;DR

This paper develops an interior penalty discontinuous Galerkin method to approximate solutions of a linear folding model, providing error estimates and validating them through numerical experiments.

Contribution

It introduces a novel finite element approach for the linear folding model with rigorous error analysis and validation.

Findings

Error estimates are established for the approximation method.

Geometric consistency errors can be controlled separately.

Numerical experiments confirm the theoretical error bounds.

Abstract

An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical analysis of the discrete model includes an a priori error estimate in case of an accurate representation of the folding curve by the isoparametric mesh. Additional estimates show that geometric consistency errors may be controlled separately if the folding arc is approximated by piecewise polynomial curves. Various numerical experiments are carried out to validate the a priori error estimate for the folding model.